1. Review of Quantum Mechanics.- 1.1 Wave Functions and Equations of Motion.- 1.1.1 States and Wave Functions.- 1.1.2 Linear Operators and Observables.- 1.1.3 The Hamiltonian and Equations of Motion.- 1.2 Symmetries.- 1.2.1 Constants of Motion and Symmetries.- 1.2.2 The Radial Schrödinger Equation.- 1.2.3 Example: The Radially Symmetric Harmonic Oscillator.- 1.3 Bound States and Unbound States.- 1.3.1 Bound States.- 1.3.2 Unbound States.- 1.3.3 Examples.- 1.3.4 Normalization of Unbound States.- 1.4 Resonances and Channels.- 1.4.1 Channels.- 1.4.2 Feshbach Resonances.- 1.4.3 Potential Resonances.- 1.5 Methods of Approximation.- 1.5.1 Time-independent Perturbation Theory.- 1.5.2 Ritz's Variational Method.- 1.5.3 Semiclassical Approximation.- 1.6 Angular Momentum and Spin.- 1.6.1 Addition of Angular Momenta.- 1.6.2 Spin.- 1.6.3 Spin-Orbit Coupling.- Problems.- References.- 2. Atoms and Ions.- 2.1 One-Electron Systems.- 2.1.1 The Hydrogen Atom.- 2.1.2 Hydrogenic Ions.- 2.1.3 The Dirac Equation.- 2.1.4 Relativistic Corrections to the Schrödinger Equation.- 2.2 Many-Electron Systems.- 2.2.1 The Hamiltonian.- 2.2.2 Pauli Principle and Slater Determinants.- 2.2.3 The Shell Structure of Atoms.- 2.2.4 Classification of Atomic Levels.- 2.3 The N-Electron Problem.- 2.3.1 The Hartree-Fock Method.- 2.3.2 Correlations and Configuration Interaction.- 2.3.3 The Thomas-Fermi Model.- 2.3.4 Density Functional Methods.- 2.4 Electromagnetic Transitions.- 2.4.1 Transitions in General, "Golden Rule".- 2.4.2 The Electromagnetic Field.- 2.4.3 Interaction Between Atom and Field.- 2.4.4 Emission and Absorption of Photons.- 2.4.5 Selection Rules.- 2.4.6 Oscillator Strengths, Sum Rules.- Problems.- References.- 3. Atomic Spectra.- 3.1 One Electron in a Modified Coulomb Potential.- 3.1.1 Rydberg Series, Quantum Defects.- 3.1.2 Seaton's Theorem, One-Channel Quantum Defect Theory.- 3.1.3 Photoabsorption and Photoionization.- 3.2 Coupled Channels.- 3.2.1 Close-Coupling Equations.- 3.2.2 Autoionizing Resonances.- 3.2.3 Configuration Interaction, Interference of Resonances.- 3.2.4 Perturbed Rydberg Series.- 3.3 Multichannel Quantum Defect Theory (MQDT).- 3.3.1 Two Coupled Coulomb Channels.- 3.3.2 The Lu-Fano Plot.- 3.3.3 More Than Two Channels.- 3.4 Atoms in External Fields.- 3.4.1 Atoms in a Static, Homogeneous Electric Field.- 3.4.2 Atoms in a Static, Homogeneous Magnetic Field.- 3.4.3 Atoms in an Oscillating Electric Field.- Problems.- References.- 4. Simple Reactions.- 4.1 Elastic Scattering.- 4.1.1 Elastic Scattering by a Short Ranged Potential.- 4.1.2 Elastic Scattering by a Pure Coulomb Potential.- 4.1.3 Elastic Scattering by a Modified Coulomb Potential, DWBA.- 4.1.4 Feshbach Projection. Optical Potential.- 4.2 Spin and Polarization.- 4.2.1 Consequences of Spin-Orbit Coupling.- 4.2.2 Application to General Pure Spin States.- 4.2.3 Application to Mixed Spin States.- 4.3 Inelastic Scattering.- 4.3.1 General Formulation.- 4.3.2 Coupled Radial Equations.- 4.3.3 Threshold Effects.- 4.3.4 An Example.- 4.4 Exit Channels with Two Unbound Electrons.- 4.4.1 General Formulation.- 4.4.2 Application to Electrons.- 4.4.3 Example.- Problems.- References.- 5. Special Topics.- 5.1 Multiphoton Absorption.- 5.1.1 Experimental Observations on Multiphoton Ionization.- 5.1.2 Calculating Ionization Probabilities via Volkov States.- 5.1.3 Calculating Ionization Probabilities via Floquet States.- 5.2 Classical Mechanics and Quantum Mechanics.- 5.2.1 Phase Space Densities.- 5.2.2 Coherent States.- 5.2.3 Coherent Wave Packets in Real Systems.- 5.3 Chaos.- 5.3.1 Chaos in Classical Mechanics.- 5.3.2 Traces of Chaos in Quantum Mechanics.- 5.3.3 Ionization of the Hydrogen Atom in a Microwave Field.- 5.3.4 The Hydrogen Atom in a Uniform Magnetic Field.- Problems.- References.- Appendix: Special Mathematical Functions.- A.1 Legendre Polynomials, Spherical Harmonics.- A.2 Laguerre Polynomials.- A.3 Bessel Functions.- A.4 Whittaker Functions, Coulomb Functions.- References.

After a brief review of quantum mechanics and a summary of conventional atomic theory, H. Friedrich discusses the structure of atomic spectra on the basis of quantum defect theory, which is treated for the first time at such a basic level in a textbook. Special attention is given to highly excited states and to the influence of external fields, which can cause intricate and interesting effects in seemingly simple systems. After a chapter on reaction theory the final chapter treats special topics such as multiphoton absorption and chaos. The book contains the kind of advanced quantum mechanics needed for practical applications in modern atomic physics. The presentation is kept deliberately simple and avoids abstract formalism as far as possible.